The 20-year-old centre back has been added to Spencer Day’s squad ahead of Saturday’s trip to Chelmsford City.
Luton-born defender Bateson has been with The Hatters since the age of eight and has captained the Under 21s, as well as training with Rob Edwards’ First Team.
Manager Spencer Day commented: “We welcome Jack from Luton.
“With our almost unknown injury situation, it’s vital we expand our squad as we are not close to being able to fill the bench currently.
“Jack is well thought of and I’m sure when he gets his chance he will be a valuable asset.”
Upon signing on loan, Jack said: “Really pleased to join Farnborough, a great club and have had a good start to the season.
“I’m looking forward to getting started and making a positive impact to the team.”
Bateson has been allocated shirt number 27.